The 52-year-old left the London club ''by mutual consent'' on Thursday, with the Dutchman soon installed as the front-runner to take the helm and reprise the caretaker manager post he filled after Luiz Felipe Scolari was sacked in 2009.
And Wilkins, whose most recent stint with the Blues' backroom team ended in 2010, reckons Hiddink - who led the club to 2009 FA Cup glory - is the ideal man for the role.
"As an interim manager, he would love the challenge, I'm sure," Wilkins said on talkSPORT.
"He would be the one person I would say would be absolutely perfect to come in to the end of the season and straighten them out."
Looking towards Saturday's visit of Sam Allardyce's Sunderland, Wilkins noted: "Sunderland aren't in the best form, they're struggling a bit, and to go the Bridge after this has happened is probably the worst place they could possibly go."
Mourinho's departure follows nine defeats in 16 league games this term - results that have caused a shocking descent into the relegation mire.
Wilkins feels the squad need to take their share of responsibility.
"I love Jose and he's done a fantastic job for Chelsea," the former England midfielder said
"He'll go elsewhere and do a wonderful job for someone.
"I honestly do believe the players need to take a lot of blame for this as well because they really haven't performed
The only player that's performed on any sort of consistent level is Willian.
"I go as much as I possibly can - I've got season tickets at Chelsea.
"With the ball, more often than not there's no problem
But without the ball they've not done half as much as they should have done
They've not worked hard enough."
The Blues take on Sunderland on Saturday and welcome Watford to Stamford Bridge on Boxing Day.
"There's got to be six points there," Wilkins added.
Hull boss Steve Bruce was saddened by Mourinho's departure and reckons the former Porto, Inter Milan and Real Madrid coach should have been given more time.
"What chance have we got, if people like Mourinho are getting sacked?" he said.
"It's sad, for me, because when he came back two, three years ago, we were all delighted to see him in our game.
"The Premier League's a better place when he's in it, surely
And his record over the last 10, 12, 15 years, whatever it is, is remarkable
Surely he's due a bad patch.
"To see it through, especially when they've got two games at home - against, no disrespect to Sunderland or Watford, but you would fancy them to get six points..
give him that chance."
Bruce added: "You hear he's lost the dressing room
They've lost nine games out of 16, so he's going to lose the dressing room - it's not going to be hunky dory."
Former England captain and Chelsea defender John Terry took to Instagram to express his thanks and regret after Mourinho's Stamford Bridge exit.
"Thank you doesn't seem enough
Sad sad day," posted Terry.
"Gonna miss you Boss
"The very best I have EVER worked with, unbelievable memories together."
Source : PA
Source: PA